Modern integrated circuits are extremely complex devices that are fabricated using equally complex processes. As the term is used herein, “integrated circuit” includes devices such as those formed on monolithic semiconducting substrates, such as those formed of group IV materials like silicon or germanium, or group III–V compounds like gallium arsenide, or mixtures of such materials. The term includes all types of devices formed, such as memory and logic, and all designs of such devices, such as MOS and bipolar. The term also comprehends applications such as flat panel displays, solar cells, and charge coupled devices. Because of the complexity of integrated circuits and the processes by which they are formed, it can be extremely difficult to determine the reasons why some devices function properly and other devices function improperly, or fail altogether.
Integrated circuits are typically manufactured on thin silicon substrates, commonly referred to as wafers. The wafer is divided up onto smaller rectangular sections for each device, typically known as the die or device. The methods and other embodiments according to the present invention can be applied to processes that are performed on other substrates to make other devices or components, such as flat panel display manufacturing, which is performed on rectangular glass substrates. Thus, this disclosure generally refers to substrates, substrate profiles, and substrate contact points, even though silicon wafer processing may be the most common application for the embodiments of the invention. It is appreciated that the same or similar methods are just as applicable to the analysis of a wide variety of substrates. Wafer test yield of die, or simply yield, is predominantly used as an example herein of an important dependent variable of interest. However, it is appreciated that any other dependent variable that is spatially associated with the substrate can also be used.
One method to assist in failure analysis is mapping important variables, such as yield, according to the position at which the variable is read on the substrate. Wafer mapping, for example, has traditionally been done by plotting the pass/fail data (i.e. yield) or other variable of interest versus the die position on the wafer. These wafer maps can be enhanced by combining values from many wafers in what is known as a stacked map. Recently there have been improvements in substrate mapping that can combine data from many wafers and many devices into what is known as a high-resolution wafer profile. Such substrate profiles are created from databases of information that is associated with substrates. A graphical representation is developed from the information, which representation depicts the yield or other variable read from the devices on the substrate, according to their position on the substrate. Substrate profiles such as these look somewhat like a topographical map, where the various contours of the profile delineate areas of different average (or otherwise computed) yield or other measured variable of interest for the devices bounded by those contours on the substrates.
Testing of yields and parametric measurement parameters on substrates has at least two purposes. One is to characterize the systematic patterns of variation across the substrate, and another is to detect outliers in these patterns that may suggest a defect of potential harm to the reliability of the die. Many techniques have been proposed to detect outliers in production test data, but Nearest Neighbor Residual has been implemented in production to detect outliers in reference to the systematic variability of data values across a substrate. Nearest Neighbor Residual uses the data from the surrounding measurements to predict whether the measurement in question is an outlier to its neighbors. The premise is that the typical value of the neighbors represents the background value of the systematic variability on that portion of the substrate.
Typical methods to identify outlier data point in substrate parametric data include simple statistics of the entire population to set a limit, and Nearest Neighbor Residual that compares a point to the median of its nearest neighbor points. Unfortunately, simple statistics on the entire population are heavily influenced by wide variations in the data, such as may be caused by the systematic variance components across the substrate. For example, a given point might be an outlier in its neighborhood, but might very nearly be an average value for the substrate, because of the wide variation of the data across the substrate. Thus, simple statistics might indicate that the point is okay, when in reality it represents an abnormality within its region of the substrate.
On the other hand, Nearest Neighbor Residual can be very limited when the nearest neighbor locations are missing or otherwise not available, such as because they are beyond the edge of the substrate. Without enough data to make a good assumption of the expected value of the region, it is difficult for Nearest Neighbor Residual to evaluate whether the point in question is an outlier.
What is needed, therefore, is a system for determining outliers that reduces some of the problems mentioned above.